Sensitivity Analyses for Race, Genotype, and Co-medication Findings

Why Sensitivity Analysis Matters

A subgroup covariate estimate depends not only on the observed pharmacokinetic data but also on how the subgroup is defined. A genotype effect can look different when genotype is coded as allele dosage rather than carrier status; a co-medication effect can change when the exposure window changes; and a race-associated contrast can depend on which categories are compared. Records with uncertain or missing classifications add another layer of choice.

A sensitivity analysis asks whether a scientific conclusion is materially changed by reasonable, explicitly stated alternatives to these choices. It is not a search for whichever definition produces the smallest p-value or the largest effect. Alternatives should be clinically or scientifically defensible, documented before interpreting their results where feasible, and compared in relation to the question each actually estimates.

The earlier material on genotype representations, medication histories, missing and misclassified records, and parameter uncertainty provides the concepts needed to define these alternatives. Here the emphasis is on comparing results systematically. Keep the population pharmacokinetic model, data exclusions, and other covariates fixed whenever possible, so that a change in the reported estimate can be attributed to the choice under examination.

Define What Is Being Compared

Suppose a model describes individual clearance \(CL_i\) using a log-linear covariate term:

Here \(CL_{\mathrm{pop}}\) is the typical clearance for the reference covariate value, \(Z_i\) is the covariate coding for individual \(i\), \(\beta\) is its coefficient, and \(\eta_i\) represents individual variability on the log scale. For a binary covariate coded 0 and 1, the clearance ratio for category 1 versus category 0 is \(\exp(\beta)\). Its percentage difference from the reference is \(100[\exp(\beta)-1]\%\). This transformation makes it easier to compare effects expressed on the log scale.

A sensitivity comparison is most interpretable when it tracks a common target contrast. However, changing a definition may change the target itself: a contrast between one race category and all remaining categories is not necessarily the same contrast as a comparison between that category and a particular reference group. In that case, report the contrast in words as well as the estimate; do not present the two estimates as if they answered an identical question.

For each alternative, record the estimate, its uncertainty, the number of individuals and observations contributing to the relevant groups, and any notable model-fitting or predictive diagnostic issues. An estimate changing slightly while its uncertainty overlaps substantially can still be practically important, or practically unimportant; the judgment depends on the magnitude and the pharmacological context, not on a significance label alone.

Varying Subgroup Definitions and Genotype Coding

Race-associated estimates require particular care in defining groups and interpreting contrasts. Race is a social classification and should not be treated as a direct measurement of genetic ancestry or as a biological mechanism. If categories are combined or a reference category is changed, state the rule and its rationale. Examine whether the conclusion is driven by a small category or by sparse representation, and avoid implying that a group label itself explains a pharmacological difference.

Genotype alternatives also encode different assumptions. Allele dosage commonly represents the number of copies of an allele, often 0, 1, or 2; a linear dosage coefficient assumes the same log-scale change for each additional copy. Carrier coding compares people with at least one copy against those with none, assuming the carrier group shares one effect. Diplotype coding can estimate separate contrasts for genotype combinations, but those contrasts may be imprecise when a diplotype is rare. The earlier tutorial on genotype representations distinguishes these codings; a sensitivity analysis compares their implications rather than treating them as interchangeable.

Varying Co-medication Windows and Uncertain Records

Medication exposure is defined in relation to time, not simply by whether a medication appears somewhere in a history. For a time-varying analysis, compare scientifically plausible windows relative to each pharmacokinetic observation or dosing event. A shorter window may capture current use; a longer window may be justified if the drug's pharmacological effect persists after the last recorded dose. The alternatives should reflect plausible exposure timing, not be chosen after inspecting which window yields the strongest estimate.

When comparing windows, check whether the exposure classification changes for many observations, whether certain subgroups are disproportionately reclassified, and whether enough exposed and unexposed information remains to estimate the effect. Keep concurrent covariates and the model specification stable. If overlapping medications or shared pathways make the effect difficult to identify, changing the window alone does not resolve that problem.

Uncertain records can be examined using more than one defensible handling rule. For example, compare a primary classification rule with a rule that excludes ambiguous records, a rule that assigns them according to a prespecified clinical criterion, or an appropriate missing-data method. Each approach relies on assumptions: exclusion may change the analyzed population; deterministic assignment may misclassify records; and imputation depends on the imputation model and its assumptions about missingness. State which records are uncertain and how each alternative treats them.

A Compact Comparison Strategy

The following sequence keeps sensitivity analyses interpretable without turning them into an unstructured collection of model fits.

For a coefficient \(\beta\) on the log-clearance scale, the effect ratio is \(\exp(\beta)\). If two otherwise comparable analyses produce coefficients \(\beta_1\) and \(\beta_2\), their ratio-scale estimates differ by the multiplicative factor \(\exp(\beta_2-\beta_1)\). This follows directly from:

For example, coefficients \(-0.10\) and \(-0.15\) correspond to ratios of approximately 0.905 and 0.861; their ratio is \(\exp(-0.05)\), approximately 0.951. The second estimate is about 4.9% lower than the first on the ratio scale. This calculation describes the difference in point estimates; it does not, by itself, quantify uncertainty in that difference.

Diagnostics, Alternatives, and Limitations

Sensitivity results need the same basic scrutiny as the primary model. Look for nonconvergence, large changes in standard errors, boundary estimates, or unstable estimates when a rare category is isolated. Check whether covariate patterns change systematically across time or patients, whether exposure groups have adequate observations, and whether predictive diagnostics worsen. A dramatic shift accompanied by a sparse subgroup or a fitting problem may reflect weak information rather than a meaningful biological difference.

The main alternative to a set of sensitivity analyses is to report one prespecified primary definition and its uncertainty. That is often clearer for a primary estimate, but it cannot show how dependent the conclusion is on plausible data or coding choices. Sensitivity analyses add that information; they do not automatically identify which definition is true. Nor do they replace careful study design, record validation, or an explicit account of confounding. In particular, a stable race-associated estimate does not show that race is a causal biological factor, and a stable co-medication association does not by itself remove confounding by indication.

A common mistake is to call an effect robust whenever it remains statistically significant under every alternative. This confuses a thresholded decision with stability of the estimated effect. An estimate can change substantially while remaining on the same side of a significance threshold, or change little while an interval crosses that threshold because precision changed. Compare estimates, uncertainty, and the scientific meaning of the contrast directly. Also avoid presenting a collection of post hoc definitions as independent confirmation: if alternatives were selected after seeing results, that selection should be disclosed.